Approximations of bi-criteria optimization problem

Abstract

In this article we study approximation methods for solving bi-criteria optimization problems. Initial problem is approximated by a new one consisting of the second order approximation of feasible set and components of objective function might be initial function, first or second approximation of it. Conditions such that efficient solution of the approximate problem will remain efficient for initial problem and reciprocally are studied. Numerical examples are developed to emphasize the importance of these conditions.

A linearized approach for solving differentiable vector optimization problems with vanishing constraints

“…We multiply (11) by 𝜇 𝑗 ≧ 0, 𝑗 ∈ J. Then, using (3) and summarizing both sides of the resulting inequalities, we get…”

“…In recent years, many researchers developed different types of algorithms and optimization techniques for solving vector optimization problems. Particular attention has been devoted to the development of new methods that solve the original mathematical (multiobjective) programming problem by means of an associated (vector) optimization problem which, in general, is easier for solving (see, e.g., Antczak [9], Chen et al [10], Duca and Duca [11,12], Miettinen [13], Ruzika and Wiecek [14], and others).…”

Second-Ordered Parametric Duality for the Multi-Objective Programming Problem in Complex Space

“…Since then, case studies on complex nonlinear, fractional, and duality programming problems have been discussed [2][3][4]. Duca formulated the vectorial optimization problem in complex space and obtained the necessary and sufficient conditions [5][6][7][8]. Datta and Bhatia started their study on a complex minimax problem in 1984 [9].…”